How to Find the Inverse of a Function

An inverse function changes the operations of what the original function will do. Replace every X and Y with the other when finding the inverse of a function with help from a math teacher in this free video on math functions and lessons.

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Video Transcript

So how do you find the inverse of a function? Hi I'm Jimmy Chang, I've been teaching college mathematics for nine years, and we're here to answer that question. Now before we start, it's important that you understand how an inverse of a function works. Now the inverse sounds like reverse, and that's exactly what an inversable function does. Is that it changes the operations, in fact it's the exact operations of what the original function will do. So we're going to go over the process real quickly, and we'll do a quick example, and to give you a glimpse as to how an inversable function works. First of all if the functions not already doing this for you, replace F of X with Y. So in other words, Y and F of X are interchangeable, so if you see a function in F of X form just replace it with Y. Now here's the most important step of them all, switch places between X and Y. That means for every X replace it with Y, and for every Y replace it with X. So X and Y literally do trade places here, that's the very most important part. Because once you switch places with X and Y you need to solve for Y, in other words you need to get Y by itself. Solve the equation and solve for Y. And last but not least, you need to replace Y with the F inverse of X. That's what the inverse function, F negative one of X. That's the inverse function notation. So here's an illustration for you. Suppose you want to find out the inverse of F of X is equal to three X plus one. Again we're going to follow the steps that we just mentioned. First, replace F of X with Y, is equal to three X plus one. Now here's the most important part, for every X and Y you switch places. In other words, for every X put Y there, for every Y put X. So your new equation is going to be X is equal to three Y plus one. Now is the time to solve for Y, get Y by itself. So first of all, subtract one, so you have X minus one is equal to three Y. And then to get Y by itself, you're going to divide by three. So you will get as a results Y is equal to X minus one over three. And then the last step, replace Y with the inverse function, but let me just go ahead and write it. So that the inverse function notation is on the left side, since that's what most people are use to seeing. So you have F inverse of X is equal to X minus one over three. So I'm Jimmy Chang, and that's an example as to how you find the inverse of a function.